Question 926763
-1,4,21,56,... ?
<pre>
Divide them by the number of term 1,2,3,4 and see what we get:

-1,2,7,14

Add 2 to those

1,4,9,16

Aha!~  The squares!  Now let's start with the squares and go backward

We ended up with the squares,

So we start with the squares, {{{n^2}}}

1,4,9,16

Before that we added 2,

So we will subtract 2,  {{{n^2-2}}}

-1,2,7,14

Before that we divided by the number of term, n

So we multiply by the number of term n,  {{{n(n^2-2)}}}

-1,4,21,56

{{{a[n]=n(n^2-2)}}}

Plug in n=1,2,3,4,5,...

-1, 4, 21, 56, 115, 204, 329, 496, 711, 980, 1309, 1704, 2171, 2716, 
3345, 4064, 4879, 5796, 6821, 7960, ... 

Edwin</pre>